[tpm]

> how they cleaned themselves after that

Water (bath), wash cloth or https://en.wikipedia.org/wiki/Strigil

[adrian_b]

None of those looks effective by itself for not leaving greasy the hands and the rest of the skin.

For thorough washing of clothes and other objects they were using lye, but lye would be too harsh for skin.

Perhaps they were first using earth to absorb most of the oil, which was then removed with the strigil, followed by washing with water.

[tpm]

They could have been using some sort of soap too, we don't really know.